TwiddleLab / Math / Functions You Can See

Model the World

Lesson 10 of 10 · 7 min · Free, no account needed

What you will learn

• To model something, measure it, pick a family (line or parabola) and fit it.
• A model makes predictions. Inside the measured range they are usually good.
• Predicting past the data is extrapolation. It can go badly wrong, so mark where your trust ends.

Start the lesson

How the lesson goes

1. Scientists, game designers and AI engineers all do one thing: turn measurements into a formula.

   Start like they do. Tap each world five times to measure it.

2. Which family fits each set of points?

   Drag each card into line or parabola. Or tap a card, then a family.

3. Fit the phone's line.

   Drag the two handles until the average miss is at the green mark or below.

4. Fit the fountain's parabola.

   Drag the vertex onto the top of the jet, then turn a until the curve runs through every point.

5. What a model can and can't do.

   A model is a formula fitted to measurements: here y = 40x + 10.

   A model makes predictions: put in an hour, get a charge.

   Predicting past the measured range is extrapolation. The formula keeps going. The world may not.

6. Leave the phone on the charger for 3 hours. What will it show?

   Drag the pin to your guess, then Check.

7. Fix the model: fence off what it doesn't know.

   Drag the fence to where the measurements end. Past it, the model only guesses.

8. An AI battery forecaster learned: charge = 100 - 8 × hours.

   It saw hours 0 to 5. Run it for later hours, up to 13. Then tap any answer that can't be true.

9. Game: forecast duel.

   Each round shows 5 measurements. Pick line or parabola; the machine fits your pick. Then the future points appear. Beat the plain line.

10. Where would you stop trusting each model?

    Tap each graph where you would stop believing the blue model. Then Check.

11. Your fountain model is y = -0.5(x - 2)² + 2. How high is the jet 1 m from the nozzle?

12. Make your model card.

    Drag your three models into the frame, each with its trust fence.

Previous lesson: Zoom In: Slope of a Curve · Part of the course: Functions You Can See

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